The present invention relates generally to thermal diffusivity measurement using laser flash techniques. More particularly, the invention relates to an improved laser flash apparatus and method which provides high accuracy at comparatively low laser power levels, so that the sample under test, and any coating applied thereto, are not appreciably degraded or damaged during the test.
In many industries, particularly in the materials industries, there is a need to accurately measure thermal diffusivity. In the semiconductor industry, for example, thermal diffusivity is an important factor in designing new substrate materials to conduct heat away from electronic components. Ceramic materials are becoming increasingly popular in this application, since these materials can demonstrate comparatively high thermal conductivity with comparatively low electrical conductivity. In developing new ceramic materials with high thermal conductivity the ability to quickly and accurately measure thermal diffusivity is quite important. With accurate and conveniently obtainable diffusivity data the ceramic engineer or scientist can more readily experiment with new formulations and fine-tune existing formulations for optimal thermal conductivity.
The flash method described by Parker in "Flash Method of Determining Thermal Diffusivity, Heat Capacity, and Thermal Conductivity," Journal of Applied Physics, 32(8), pages 1679-1684 (1961), W. J. Parker, R. J. Jenkins, C. P. Butler and G. L. Abbott, remains the most commonly used technique for measuring thermal diffusivity.
Briefly, the Parker method employs a thermal pulse source in the form of a flash tube (lasers are commonly used today) to apply a thermal pulse to one surface or portion of the sample under test. The thermal pulse propagates through the sample, manifesting itself as a temperature variation in the sample over time. A temperature sensor, such as a thermocouple contact sensor or an infrared noncontact sensor, senses a temperature rise on the rear surface or portion of the sample, which is indicative of the thermal diffusivity of the sample. The sensor output is fed to an oscilliscope to which a camera is attached for photographing the oscilliscope waveform. The waveform represents the temperature variation as a function of time. Diffusivity is then calculated based on the one-half time (t.sub.1/2), that is, the time taken for the temperature to rise halfway between the ambient starting temperature and the final temperature, as revealed in the photograph of the oscilloscope waveform. The relationship between one-half time and diffusivity may be expressed by the following equation: ##EQU1## where .alpha. is the diffusivity and L is the sample thickness.
Thermal conductivity (K) is the product is diffusivity (.alpha.), the density .rho.) and the heat capacity (C.sub.p): EQU K=.alpha.C.sub.p .rho. (2)
In implementing the Parker flash method care must be taken to prevent the initial heat pulse of the radiant energy source from directly illuminating the sensor, since this could alter the ability of the sensor to accurately respond to the temperature rise as it diffuses or propagates through the sample. With completely opaque samples careful masking is generally sufficient to prevent direct sensor illumination. However, translucent or transparent materials present a problem. Direct optical illumination of the sensor through the sample can disturb the sensor reading and obfuscate the relevant temperature rise data.
One proposed solution has been to coat the translucent or transparent sample with an opaque material. Another solution has been to restrict testing to samples of sufficient thickness such that optical transmission through the sample is greatly attenuated. Both of these approaches have been far from satisfactory.
Ceramic substrates of the type presently used in the semiconductor industry are comparatively thin (on the order of 25 to 40/1000ths of an inch) and are often not fully opaque at these thicknesses. Optical transmission through these samples is problematic and can adversely affect the sensor and alter or disturb the diffusivity data. Providing the ceramic substrate with a coating of opaque material will, of course, prevent optical transmission from interfering with the sensor, although there has been a considerable problem with the laser energy destroying the coating and thereby exposing the sensor to unwanted illumination.
Attempts at lowering the power of the laser have not heretofore been successful since lowering the laser power also lowers the heat pulse signal relative to the noise level of the measurement system. In addition, most attempts at lowering the laser power have involved lowering the laser power supply excitation, which changes the pulse shape of the laser and adversely affects the accuracy of the measurement.
The present invention overcomes the coating destruction problem by advantageously utilizing a low power laser as a radiant energy heat pulse source. The laser employed in the presently preferred embodiment develops an output heat pulse on the order of 0.7 joules, in contrast with the significantly higher powered lasers used in conventional flash methods. For example, Parker used a flash tube dissipating 400 joules of energy in each flash. A more recent publication described a modified Parker technique using a ruby laser producing 3 joules of energy. See Yutaka Tada et al., "Laser Flash Method for Measuring Thermal Conductivity of Liquids-Application to Low Thermal Conductivity Liquids," Rev. Sci. Instrum., Vol. 49, No. 9, pp. 1305-1313, September 1978.
The present invention is able to use inexpensive and nondestructive low power laser sources by means of a sophisticated signal processing technique whereby a plurality of temporally spaced low power radiant energy pulses are applied to a first portion (e.g. front surface) of the sample, each pulse causing a temperature rise to propagate through the sample to a second portion (e.g. rear surface). The temperature rise associated with each pulse is individually sensed, preferably using a noncontact infrared sensor, and electrically recorded as data in a two-state memory device such as the random access memory of a computer. The data is then statistically processed to derive a set of favored values indicative of the temperature of the second portion of the sample as a function of time. Preferably the statistical processing includes signal averaging of the sensed data.
In the presently preferred embodiment approximately 1000 data samples are taken during the relevant time period which is a function of the rise time of the thermal signal (from the onset of the thermal pulse until approximately three to four t.sub.1/2 times thereafter) for each pulse. A plurality of single shot pulses are applied to the sample in succession and the data acquired after each pulse is coded and averaged. Although the thermal pulse signal power at a 0.7 joule output is quite low, the received signal at the sensor is greatly enhanced by the statistical processing. This results from the fact that random signals and noise in the measurement system tends to cancel out when averaged over a number of iterations, whereas the signal of interest resulting from the heat pulse propagation tends to add constructively with successive iterations. Thus the statistical processing greatly improves the signal-to-noise ratio and allows the acquisition of good thermal data using the low power heat source.
The statistically processed data, representing a set of favored values indicative of the temperature of the second surface or portion as a function of time, is then further processed to determine the diffusivity of the sample. In the presently preferred embodiment a least squares curve-fitting algorithm is applied to the favored values data and the curve fit is optimized to the data by adjusting numerical parameters indicative of the thermal diffusivity. In the preferred embodiment the least squares curve fit algorithm is used based on the a priori assumption that the data will fit a curve defined by the following equation representing sensor reading as a function of time with diffusivity being an adjustable parameter: EQU f(x)=c+b(1=2exp(-ax)+2exp(-4ax)) (3)
where (c) is the baseline of the curve, (b) is the amplitude of the curve and (a) is directly related to the diffusivity (.alpha.) by the equation: EQU .alpha.=a(L/.pi.) (4)
The curve-fitting algorithm as well as the statistical processing may be performed by a digital computer with the diffusivity parameter (.alpha.) yielding the desired numerical end result.
For a more complete understanding of the invention, its objects and advantages, refer to the following specification and to the accompanying drawings.